And this error is so egregious that I am confounded at the
universality with which it has been received. Mathematical axioms are
_not_ axioms of general truth. What is true of _relation_--of form and
quantity--is often grossly false in regard to morals, for example. In
this latter science it is very usually _un_true that the aggregated
parts are equal to the whole. In chemistry also the axiom fails. In
the consideration of motive it fails; for two motives, each of a given
value, have not, necessarily, a value when united, equal to the sum of
their values apart. There are numerous other mathematical truths which
are only truths within the limits of _relation_. But the mathematician
argues, from his _finite truths_, through habit, as if they were of an
absolutely general applicability--as the world indeed imagines them to
be. Bryant, in his very learned 'Mythology,' mentions an analogous
source of error, when he says that 'although the Pagan fables are not
believed, yet we forget ourselves continually, and make inferences
from them as existing realities.' With the algebraists, however, who
are Pagans themselves, the 'Pagan fables' _are_ believed, and the
inferences are made, not so much through lapse of memory, as through
an unaccountable addling of the brains. In short, I neyer yet
encountered the mere mathematician who could be trusted out of equal
roots, or one who did not clandestinely hold it as a point of his
faith that _x??+px_ was absolutely and unconditionally equal to _q_.
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